Subject Code & Name: MA25C02 – Linear Algebra
Regulation: R-2025
Semester: II (Second Semester)
Branch: B.E. CSE (CSE)
Credits / L-T-P: 4 Credits | L-T-P: 3-1-0
Course Objectives
- To impart foundational knowledge in linear algebra essential for analysing and solving problems in engineering applications.
- To provide the knowledge on computation using software and interpret key linear algebra concepts using software.
Full Unit-wise Syllabus
Unit I – Vector Spaces
Introduction to Vector Spaces, Examples, Subspaces, Linear Combinations, Span, Generating Sets, Linear Dependence and Independence, Basis and Dimension, Dimension of Subspaces.
Activities: Open-Source software, exercises to test linear dependence and independence using rank, compute span and basis of a set of vectors, determine the dimension of subspaces, and illustrate the concept of subspace and basis in R²/R³ with visualization.
Unit II – Linear Transformations and Diagonalization
Null space, Range, Dimension Theorem (statement only), Matrix representation of a linear transformation, Eigenvalues & Eigenvectors, Diagonalizability.
Activities: Open-Source software, exercises to compute the matrix representation of a linear transformation, find the null space and range of a matrix, and compute eigenvalues and eigenvectors of a matrix.
Unit III – Inner Product Spaces
Inner product, Norms, Cauchy–Schwarz inequality, Gram–Schmidt orthogonalization, Simple problems (up to R³).
Activities: Open-Source software, exercises to compute inner products and vector norms.
Unit IV – Matrix Decomposition
Orthogonal transformation of a symmetric matrix to diagonal form – Positive definite matrices, QR decomposition, Singular Value Decomposition (SVD), Least squares solutions – simple problems (up to 3 × 3 matrices).
Activities: Open-Source software, exercises to check if a matrix is positive definite, perform QR decomposition and SVD using built-in functions.
Course Outcomes (COs)
- CO1: Explain the fundamental concepts of Linear Algebra.
- CO2: Compute and interpret eigenvalues and eigenvectors.
- CO3: Apply inner product concepts and perform orthogonalization.
- CO4: Compute least squares solutions of linear system of equations.
- CO5: Use MATLAB to implement and validate key linear algebra concepts.
Assessment Pattern (Quick Note)
- Weightage: Continuous Assessment 40% | End Semester Examinations 60%
- Internal methodology: Assignment (20%), Software activity (20%), Quiz (20%), Internal Examinations (40%)
Source: Official Anna University B.E. Computer Science and Engineering R-2025 Syllabus
Last Updated: September 2026
Comments
Post a Comment